It won't likely trigger a nuclear war. It would trigger a conventional war that would see NATO forces directly confront the Russian military and attempt to push it back out of the Baltics (and try to inflict severe damage if Russia refuses).

Neither side with nukes would be fighting for survival and would not jump to nuclear threats or exchange until or unless their own existing territory was at risk of annexation / loss.

Russia would shift to a nuclear warning posture if pushed back to their borders. If NATO pursued and threatened territory taking, Russia would threaten nuclear response at that point, especially if it was in a particularly weakened condition or believed it couldn't hold its ground.

On the NATO side, there's practically no threat of the US, France or the UK losing territory to Russia in a Baltic-focused conflict (or in Eastern Europe for that matter). To draw a nuclear threat from NATO would similarly require the nuclear powers to be under threat of losing their own territory (and they'd probably have to believe they can't hold their ground). The UK isn't killing ten plus million of its people in a nuclear exchange with Russia for the sake of Estonia, Latvia or Lithuania's territorial integrity as nation-states.

I think the only way that gets nuclear is if Russia plays the crazy card and proclaims that it now regards the annexed Baltic territory as its own and puts up the nuclear warning then and there (move in, take territory, immediately raise the crazy nuclear flag, test the resolve & risk aversion of the other side to respond militarily once the nuclear flag is out of the box). Then NATO has to decide if it believes Russia will actually act crazy.

Doubt it. It would trigger a cold war II but not a nuclear war.

The baltic states can not be defended militarily. If Ukraine were in the EU, would be a different thing.

That was probably true 4 years ago. It's not at all obviously true today.

Er no, Ukraine was supposedly protected by the Budapest Declaration.

One of the signatories was the invader, the rest found obtuse reasons why they didn't have to defend Ukraine.

The next annexation will be the same.

Russia could have annexed the Baltic states when they secceded in 91, but chose not to. From their perspective, they had enough of empire and grew tired of propping the periphery. There was no need for these states to join Nato, and they could have remained as independant partners benefitting from trade with 2 blocks. The fact they chose to move away from Russia has more to do with corruption than logic.